In the jet engine literature there is a chain of misleading conclusions in the representation of the force balance for the hovering flight of lift engines such as helicopter rotors and jet engines at static thrust conditions on test rigs. Engineering knowledge is an accumulation of approximations and one has to be aware of the degree of allowable approximations. I am concerned here only with errors which can reduce the thrust predictions in the range of 20% (test rig measurements of jet engines) and in the range of 100% (cylindrically shrouded lift fans, as applied to some known VTOL prototypes of the 1960's).
Because of these errors in vertical takeoff and landing (VTOL) aircraft theory, mistakes have been made in the design of the aircraft which, in part, I am able to remedy with the present invention. Before explaining the invention, however, it is important to develop both the errors in existing theory and the contribution of the prior art to the development of engine fan and fan shroud assemblies.
The failures in the force balance of hovering lift engines and static thrust definitions include five points A through D:
A. An excessively simplified propeller theory, from Froude and Rankine for the case of vertical hovering with free (unshrouded) propellers.
When the momentum laws are applied, the control area at the propeller entrance is treated as being moved to infinity in order to be able to say that "the control area inlet velocity is approaching zero value and hence the inlet momentum is also approaching zero value."
This is an oversimplified statement. One can never move the control area to infinity and forget the underpressure forces on it at the same time, if one applies the momentum laws for a force balance on a subject (jet engine) inside the control area. Misleading conclusions can occur already even when the control area is treated as being at a generous distance from the subject of the examination, as illustrated under point B below. Theoretically, one can draw the control area at any distance including infinity around the considered subject. One will gain different force components for each control area definition. But the resultant inlet force must always be the same, if no major component is "forgotten". It must be also the same resultant force in infinity.
The state-of-the-art propeller theory has overlooked the inlet momentum in front of the propeller and in front of jet engines in the hovering condition and the thrust supporting underpressure force at the same place which compensates partially the inlet momentum force.
This compensation would be theoretically exactly an 1/2 part of the inlet momentum force, if the stream line would flow in parallel through a cylindrical inlet duct of a jet engine and if the inlet force balance is made on a closely to the inlet drawn control surface. The remaining effective half of the braking inlet momentum force is the resultant inlet force, acting along the jet engine axis. If one moves the control surface of any shape to infinity upstream of the jet engine inlet, including any inlet stream line picture, this resulting inlet force can never disappear, when moved along it's acting line in contrast to faulty static thrust theory in the present state of the art literature. Faulty static thrust theory takes regard only to the diminishing inlet momentum force, when the control surface is moved to infinity. Faulty theory overlooks that the diminishing inlet momentum force component is only replaced by an additional underpressure force component rising on the backside projection of the growing control surface balloon, when the border transition to infinity is made. This backside is defined in a view from infinity towards the engine inlet seen along the engine axis. Underpressure forces have determined values also on a big control surface in infinity, because the diminishing underpressure is compensated by the increasing surface area of the control surface. The basic law of mechanics, that a force cannot disappear when moved along its acting line supplies the border condition for the integral "pressure difference times area vector element" which hence is not undetermined. Furthermore overlooks faulty VTOL and static thrust theory the counterdependence between the momentum forces and underpressure forces between the adjacent stream surfaces (which appear as stream lines in two dimensional pictures) given by the Energy Law Equation (Bernoulli) and the Continuity Law Equation.
Furthermore existing analysis techniques have overlooked the centrifugal force caused by the curved stream lines acting on the control surface. The only force taken into consideration in the state-of-the-art propeller theory for the static thrust case is the exit momentum force m c.sub.a =F downstream of the propeller, where the jet is contracted to a cylindrical shape.
The jet energy is roughly m c.sub.a.sup.2 /2 or the supplied engine power is 1/.eta.m c.sub.a.sup.2 /2=p. Hence, according to standard propeller theory the ratio Lift/Power=F/P=.eta.(2/c.sub.a). This is wrong.
I have reported a corrected theory derived with a control surface closely drawn to the propeller and without omitting essential forces, which shows that EQU F/P=.eta.(1.7/c.sub.a) EQU instead of EQU F/P=.eta.(2/c.sub.a)
for free helicopter rotors. The factor "1.7" represents the influence of geometry. Using this value, modern helicopter rotors have a more believable calculated efficiency of approximately 0.75 instead of 0.55 calculated by the old unmodified theory.
B. The factor "2" in F/P=.eta.2/c.sub.a which actually is already questionable for helicopter rotors, as noted in point A, is transferred to all other lift configurations in the criticized VTOL-theory.
For example, this factor has been applied to cylindrically shrouded fans which were the lift engines for a number of well known VTOL-projects in the 1960's.
Actually the factor "2" must be replaced by other numbers or coefficients for each different lift engine geometry, derived theoretically from a control surface for the application of momentum laws as close as possible to that of the engine under consideration.
Cylindrically shrouded fans should have an idealized geometry factor of "1" instead of "2", as I have shown in my paper "Comparison of Lift Concepts", which means a 100% difference and half of the expected lift force at a given engine power compared to the questionable state of the art theory. This significant mistake is found in papers of authors employed at companies who made VTOL aircrafts with cylindrically shrouded fans.
C. Another defect in the standard theory is the neglect of the considerable inlet forces, resulting in an not permissible excessively simplified thrust equation for jet engines: EQU T=m (ca-co)
where
mc.sub.a =Exit momentum force PA1 mc.sub.o =Inlet momentum force PA1 T=Thrust during forward flight PA1 m=Mass flow rate per second PA1 c.sub.a =Nozzle exit velocity PA1 c.sub.o =Flight velocity, sometimes
designated as c.
Even if one agrees to neglect engine nacelle forces, the mass increment at the exit due to added fuel (an error of 1 to 3%), and if one assumes the presence of a cylindrical exit jet (no static pressure thrust) there is still a 15 to 20% error in this equation. The latter error stems from the neglect of centrifugal forces acting on the curved stream lines in front of the engine if one moves the control surface as so far foward, that m c.sub.o is the inlet momentum. The suction velocity of the jet engine usually is only 0.6 times the value of the flight velocity which is close to the sound barrier. Hence, there results a conical expansion of the suction jet causing the centrifugal forces.
The thrust equation T=m (c.sub.a -c.sub.o), which is used also in many papers of the jet engine industry, is actually valid only for the case where the flight velocity c.sub.o is equal to jet engine entrance velocity, that is at about 300 mph at usual layouts of jet engines.
The validity of this equation cannot be expanded to flight velocities of 980 km/h by means of a simple forward move of the entrance control surface to a place where the velocity of the suction jet is equal to c.sub.o, because one cannot neglect other forces, caused by this forward move.
D. Chief among the improper conclusions arising from the excessive simplified thrust equation T=m(c.sub.a -c.sub.o) is that the prior static thrust value can be derived from this equation.
The literature often states that "Flight velocity c.sub.o is equal to zero at static thrust condition therefore T=m c.sub.a ". T=m c.sub.a is called "gross thrust" (Brutto-Schub). In actuality this is not the static thrust of a jet engine as it beings take-off on a runway. Still to be considered must be the inlet velocity at static thrust condition dictated by the air foil geometry of the compressor and the compressor speed. This inlet velocity imparts a braking inlet momentum and an underpressure thrust supporting force compensating the inlet momentum only to approximately half of its value where the jet engine inlet duct is approximately cylindrical.
E. The view that T=mc.sub.a fully represents the "generated force" of a lift engine in hovering condition and the static thrust of a jet engine has several bases as mentioned under point D. Prior art proof of these views rest upon jet engine evaluations in test rigs. However, it is here pointed out that the jet engine test rigs were not fitted with nacelles as in real aircraft. Test rig engines have an inlet fairing (bell mouth, inlet shield) and therefore the force balance on a test rig is very different from that of an engine mounted in an aircraft nacelle. Actually the axial component of the underpressure force acting on the inlet fairing has to be added to the exit momentum thrust mc.sub.a instead of being considered as a part of mc.sub.a.
This incorrect belief is widespread in the art. It is seen in the literature through the photographs of engines on their test rigs. There are plenty of wirings for measurements on all places, but none on the inlet fairing which is rigidly attached to the jet engine. Evidently the art believes that the suction force on the inlet fairing is part of mc.sub.a and therefore it is not necessary to determine it separately. Fortunately this force acting on the inlet shield can be added to the exit momentum thrust mc.sub.a. Theoretically one can derive this with a force balance based on a control surface for the application of momentum laws closely approaching the engine surface, considering the inlet fairing as part of the engine.
Beside small losses due to curved inlet flow, one can obtain this underpressure force on the inlet shield without additional engine power beside the power m c.sub.a .sup.2 /2, which is the concomittant for the exit thrust mc.sub.a. Theoretically one can prove this basic concept of the radial and tangential force balance acting on the curved inlet stream lines, being aware that the underpressure generating centrifugal force is normal to the stream line tangent and hence causes no force component in the tangential direction. Thus it does not influence the power need for the acceleration of fluid particles from zero velocity to c.sub.a. This basic concept is missing in the literature apart from my contributions noted earlier.
Two other forces act upon the inlet area of testing engines. There is the inlet momentum mc.sub.1 acting across the first stage compressor entrance area as a braking force, which amounts approximately to twice the positive thrust supporting underpressure force acting on the inlet fairing. This inlet momentum force is reduced again to half of its effective value by means of the underpressure force over the first stage compressor area which is in accord with the Bernoulli equation ##EQU1## where .rho. air density and A.sub.r =the compressor first stage entrance area.
The remaining half of the braking inlet momentum force is by accident approximately compensated by the inlet fairing suction force as I have theoretically derived in various papers. This compensation corresponds to the accidental dimensions of the inlet as used on test rigs. Hence three forces approximately compensate one another at the test engine air entrance on the test rig, i.e. the inlet momentum force is approximately compensated by one half through means of the underpressure force in front of the first stage compressor rotor and by the other half through means of the inlet fairing underpressure. The only force acting on the test rig with cylindrical exhaust jet appears to be the exit momentum thrust m c.sub.a. Therefrom arise the misleading concepts discussions under points B and D above which are stated in terms of "test rig experience."
Under varying geometric configurations, as in the drawing of the present disclosure, the forces at the engine entrance will also vary and do therefore not compensate each other and must therefore be taken into account.
I have suggested that F/P be defined as F/P=.eta.f.sub.G (1/c.sub.a) where f.sub.G is the "Geometry Factor"--the influence of geometry, 1/c.sub.a is the influence of exit velocity niveau level and .eta. is the overall efficiency. This replaces the erroneous correlation F/P=(2/c.sub.a), where the number "2" is even not correct for hovering propellers but is mistakingly applied to any lift engine which accelerates air downwards. Actually this number has to change at different geometries. This number, f.sub.G, the "Geometry Factor" can reach the value of "3" at FIG. 3 and can increase up to "6" at FIG. 1. But it is never a constant exclusively of the value "2".
With cylindrically shrouded lift fans the geometry factor f.sub.G reaches the value "1" instead of the erroneous value "2" as it appears in papers of companies who have built such cylindrically shrouded fans based on the wrong theory of these papers. The moderate performance has been explained as a matter of efficiencies.